Warp Core Power Generation

(To be Updated)

In "True Q"[TNG6], we hear the following exchange occur in Engineering:

Amanda: "It's hard to imagine how much energy is being harnessed in
there."
Data : "Imagination is not necessary; the scale is readily quantifiable.
We are presently generating 12.75 billion gigawatts per . . . "

At that point, Data is cut off, leaving us hanging. Warsies contend
that the quote is absolutely meaningless. As the basis
of this, they point out the following facts:

1. Amanda refers to energy, but Data rattles off a figure in watts.
Energy is measured in joules, with watts referring to power (energy over
time).
2. "Gigawatts per" anything is a very peculiar phrasing, and
watts per second would have to imply an increase in power.

The problem is that the above points do not render the entire quote
meaningless. First, conversion of watts to joules and vice versa is a
simple affair . . . a watt is a joule per second. Second, although "watts
per" anything is a peculiar phrasing, it is not unheard of. A
quick search
through Yahoo provides numerous examples of this use where "anything"
is a time unit, in a manner similar to the "kilowatt-hours" on most
people's power bills. It does not imply an accelerating increase in
energy. "Watts per X" is also used to denote intensity
(watts per square meter), or power production per amount of fuel.

Opponents have then argued that I simply assumed that Data was
about to offer a time unit. However, this is incorrect.

I am not assuming it is a unit of time. It is the only continuation of
the sentence that makes sense (or, more correctly, "comes close to making
sense") in the context. It is also (note well) the
continuation that offers the smallest possible interpretation of
the power figure given. Further, it also happens to correspond with the
script (which, alas, is non-canon), where Data says "per second."

But, let's look at the other possibilities anyway:

Now, when Amanda says "in there" she referred to the warp core, so
perhaps Data (being Data) was going to give her a power-by-unit-volume
analysis. However, the largest volume he could logically use would be the
warp core, so any smaller chunks of it would increase the total power.

It is possible, though less likely, that he was giving her a
power-generation-by-fuel-consumption report, though this does not fit the
context. Besides, proton/antiproton reactions liberate 90,000 gigajoules
per gram of antimatter. To achieve 12.75 billion gigawatts, they would
need something like 140 kilograms of antimatter per second, with an equal
amount of matter, flowing through the reactor. (This assumes, of course,
that there's no such thing as Trek
uber-antimatter (which I don't think there is, but I thought it worthy
of note here).)

If this 140kg of antimatter were somehow rigged at the same average
density as a human being, this would be the equivalent of two rather
chunky guys . . . say, Homer Simpson . . . slamming into each other each
second.

There are problems with this idea.

1. There isn't room for two Homer Simpsons in the warp core. I'm not
even sure he could fit down the pipes leading to the core, even if you
buttered him. Seriously, though, two Homers per second is an awful lot
of stuff to be in that core, even though it wouldn't be there all at once.
I'm not even sure you could get each proton to react with each antiproton
in such a situation (which would mean you would need even more than two
Homers, compounding the problem).
1a. The dilithium crystals through which everything is channelled are
awfully small to be dealing with two Homers per second.

Enterprise-D dilithium crystals

2. 140 kilograms per second would be 504,000 kilograms per hour,
84,672,000 kilograms per week, and 4,415,040,000 kilograms per year . . .
and that's just the antimatter. Unless the Federation is full of
antimatter gas stations, that isn't going to work.
2a. Using this reprint
of a screen from "Contagion"[TNG] (which I
use because it is similar to the MSD, but labelled), you can see that
there
isn't a lot of room devoted to antimatter containment. But, even if they
were to somehow store antimatter with a density like that of iron, they'd
need 630,720 m^3 for a year's supply. That would pretty much fill the
entire volume of the engineering hull behind the warp core.
2b. Voyager went a long time without needing antimatter. In fact, I'm
not sure they ever got any.

3. To power the Hathaway in "Peak Performance"[TNG], Wesley beamed
over a small container of antimatter that he'd been using as a part
of a science experiment. This not only gave the Hathaway sufficient power
to engage in the wargames, but also gave her the energy necessary to
engage warp drive.

Wesley's Antimatter (blue candle wax)

So, that just doesn't work (unless you go for Trek uber-antimatter).
On the other hand, if the ship was only generating 12.75 billion gigawatts
per day (as I suggested), that's "only" 147,000 gigajoules per second, or
about 1.5 grams of antimatter (and an equal amount of matter) per second.

Given the size of Wesley's container, I'd call this a pretty fair
guess, assuming the Hathaway didn't need as much power, and was on
low-power mode anyway.

On the other hand, we have the following scene from "Revulsion"[VOY]:

Seven : "The optical assembly is properly aligned. I am ready to access
the main power supply."
Kim : "After you."
(The pair climb down, and Seven begins to reach into a conduit)
Kim : "Wait! What are you doing, there are five million gigawatts
running through there!"
Seven : "The exoskeleton on this limb can withstand it."

This gives a lower limit of 5,000,000 gigajoules (5,000 terajoules) per
second for Voyager's power generation abilities, or 34 times my 147
terajoules/second figure for the Enterprise-D. This could either imply
that the Enterprise-D was on a very low-power mode, or that my use of the
term "day" is incorrect, and that something like "hour" (which, obviously,
would result in a figure 24 times higher) would be more appropriate.

Some dispute such figures, pointing instead to "The Dauphin"[TNG]:

Data: "Sir, sensors indicate the communication originated from a
terawatt source on the planet."
Riker: "That's more power than our entire ship can generate."
Data: "It is what is needed to penetrate the atmosphere."

However, there are several better things that can be done here than to
throw out every other quote in favor of the quote from "The Dauphin".
First, take a look at the context . . . they're talking about
communications. We know from ST:TMP, et cetera, that starships carry not
only subspace communications equipment, but also devices capable of
transmitting via "primitive" radio frequencies, so one could argue that by
"entire ship" Riker was employing a synecdoche. This can be
reasonably well established, given that we know from "Who
Watches the Watchers"[TNG] that a 4.2 gigawatt reactor can power a
subspace relay station. It is likely, therefore, that the ship's entire
complement of communications equipment can't send signals with a
terawatt of power behind them, and that therefore Riker did not refer to
the entire power generation capabilities of the starship Enterprise.

This allows us to fit the "Dauphin" quote into the numerous other
examples, and not simply throw it away in light of the preponderance of
evidence. It also provides a better solution than throwing away the
preponderance of evidence in favor of a single quote.

Update: An alert reader noticed a slip-up regarding the 140 kg
figure. The warp core only needs one Homer per second, not
two. I inadvertently doubled the proper figure. I'll take care
of that in the planned re-writing of the page.